9x^2+30x+9=x^2+10x+81

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Solution for 9x^2+30x+9=x^2+10x+81 equation: 


Simplifying
9x2 + 30x + 9 = x2 + 10x + 81

Reorder the terms:
9 + 30x + 9x2 = x2 + 10x + 81

Reorder the terms:
9 + 30x + 9x2 = 81 + 10x + x2

Solving
9 + 30x + 9x2 = 81 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -81 + 30x + -10x + 9x2 + -1x2 = 81 + 10x + x2 + -81 + -10x + -1x2

Combine like terms: 9 + -81 = -72
-72 + 30x + -10x + 9x2 + -1x2 = 81 + 10x + x2 + -81 + -10x + -1x2

Combine like terms: 30x + -10x = 20x
-72 + 20x + 9x2 + -1x2 = 81 + 10x + x2 + -81 + -10x + -1x2

Combine like terms: 9x2 + -1x2 = 8x2
-72 + 20x + 8x2 = 81 + 10x + x2 + -81 + -10x + -1x2

Reorder the terms:
-72 + 20x + 8x2 = 81 + -81 + 10x + -10x + x2 + -1x2

Combine like terms: 81 + -81 = 0
-72 + 20x + 8x2 = 0 + 10x + -10x + x2 + -1x2
-72 + 20x + 8x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-72 + 20x + 8x2 = 0 + x2 + -1x2
-72 + 20x + 8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-72 + 20x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 5x + 2x2) = 0

Factor a trinomial.
4((-9 + -2x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4.5, 2}

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